| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward Further Pure 1 question testing basic complex number operations: scalar multiplication, subtraction, conjugation, and division. While FP1 content is inherently more advanced than Core modules, these are routine mechanical procedures requiring only standard techniques (multiplying by conjugate for division). The question demands accuracy but no problem-solving insight, making it easier than average even for A-level standards. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(-12 + 13i\) | B1B1 2 | Real and imaginary parts correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| B1 | \(z^*\) seen | |
| M1 | Multiply by \(w^*\) | |
| \(\frac{27}{37} - \frac{14}{37}i\) | A1 | Obtain correct real part or numerator |
| A1 4 | Obtain correct imaginary part or denom.; sufficient working must be shown |
## Question 2:
**Part (i)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $-12 + 13i$ | B1B1 **2** | Real and imaginary parts correct |
**Part (ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| | B1 | $z^*$ seen |
| | M1 | Multiply by $w^*$ |
| $\frac{27}{37} - \frac{14}{37}i$ | A1 | Obtain correct real part or numerator |
| | A1 **4** | Obtain correct imaginary part or denom.; sufficient working must be shown |
---2 The complex numbers $z$ and $w$ are given by $z = 4 + 3 \mathrm { i }$ and $w = 6 - \mathrm { i }$. Giving your answers in the form $x + \mathrm { i } y$ and showing clearly how you obtain them, find\\
(i) $3 z - 4 w$,\\
(ii) $\frac { z ^ { * } } { w }$.
\hfill \mbox{\textit{OCR FP1 2011 Q2 [6]}}